{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article7862","name":"Geometric Spanners for Points Inside a Polygonal Domain","abstract":"Let P be a set of n points inside a polygonal domain D. A polygonal domain with h holes (or obstacles) consists of h disjoint polygonal obstacles surrounded by a simple polygon which itself acts as an obstacle. We first study t-spanners for the set P with respect to the geodesic distance function d where for any two points p and q, d(p,q) is equal to the Euclidean length of the shortest path from p to q that avoids the obstacles interiors. For a case where the polygonal domain is a simple polygon (i.e., h=0), we construct a (sqrt(10)+eps)-spanner that has O(n log^2 n) edges where eps is the a given positive real number. For a case where there are h holes, our construction gives a (5+eps)-spanner with the size of O(sqrt(h) n log^2 n).\r\n \r\nMoreover, we study t-spanners for the visibility graph of P (VG(P), for short) with respect to a hole-free polygonal domain D. The graph VG(P) is not necessarily a complete graph or even connected. In this case, we propose an algorithm that constructs a (3+eps)-spanner of size almost O(n^{4\/3}). In addition, we show that there is a set P of n points such that any (3-eps)-spanner of VG(P) must contain almost n^2 edges.","keywords":["Geometric Spanners","Polygonal Domain","Visibility Graph"],"author":[{"@type":"Person","name":"Abam, Mohammad Ali","givenName":"Mohammad Ali","familyName":"Abam"},{"@type":"Person","name":"Adeli, Marjan","givenName":"Marjan","familyName":"Adeli"},{"@type":"Person","name":"Homapour, Hamid","givenName":"Hamid","familyName":"Homapour"},{"@type":"Person","name":"Asadollahpoor, Pooya Zafar","givenName":"Pooya Zafar","familyName":"Asadollahpoor"}],"position":17,"pageStart":186,"pageEnd":197,"dateCreated":"2015-06-12","datePublished":"2015-06-12","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Abam, Mohammad Ali","givenName":"Mohammad Ali","familyName":"Abam"},{"@type":"Person","name":"Adeli, Marjan","givenName":"Marjan","familyName":"Adeli"},{"@type":"Person","name":"Homapour, Hamid","givenName":"Hamid","familyName":"Homapour"},{"@type":"Person","name":"Asadollahpoor, Pooya Zafar","givenName":"Pooya Zafar","familyName":"Asadollahpoor"}],"copyrightYear":"2015","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.SOCG.2015.186","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6237","volumeNumber":34,"name":"31st International Symposium on Computational Geometry (SoCG 2015)","dateCreated":"2015-06-12","datePublished":"2015-06-12","editor":[{"@type":"Person","name":"Arge, Lars","givenName":"Lars","familyName":"Arge"},{"@type":"Person","name":"Pach, J\u00e1nos","givenName":"J\u00e1nos","familyName":"Pach"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article7862","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6237"}}}